7+5x-3x^2=-6.4

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Solution for 7+5x-3x^2=-6.4 equation:


Simplifying
7 + 5x + -3x2 = -6.4

Solving
7 + 5x + -3x2 = -6.4

Solving for variable 'x'.

Reorder the terms:
7 + 6.4 + 5x + -3x2 = -6.4 + 6.4

Combine like terms: 7 + 6.4 = 13.4
13.4 + 5x + -3x2 = -6.4 + 6.4

Combine like terms: -6.4 + 6.4 = 0.0
13.4 + 5x + -3x2 = 0.0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-4.466666667 + -1.666666667x + x2 = 0.0

Move the constant term to the right:

Add '4.466666667' to each side of the equation.
-4.466666667 + -1.666666667x + 4.466666667 + x2 = 0.0 + 4.466666667

Reorder the terms:
-4.466666667 + 4.466666667 + -1.666666667x + x2 = 0.0 + 4.466666667

Combine like terms: -4.466666667 + 4.466666667 = 0.000000000
0.000000000 + -1.666666667x + x2 = 0.0 + 4.466666667
-1.666666667x + x2 = 0.0 + 4.466666667

Combine like terms: 0.0 + 4.466666667 = 4.466666667
-1.666666667x + x2 = 4.466666667

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = 4.466666667 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = 4.466666667 + 0.6944444447

Combine like terms: 4.466666667 + 0.6944444447 = 5.1611111117
0.6944444447 + -1.666666667x + x2 = 5.1611111117

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 5.1611111117

Calculate the square root of the right side: 2.271807895

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 2.271807895 and -2.271807895.

Subproblem 1

x + -0.8333333335 = 2.271807895 Simplifying x + -0.8333333335 = 2.271807895 Reorder the terms: -0.8333333335 + x = 2.271807895 Solving -0.8333333335 + x = 2.271807895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 2.271807895 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 2.271807895 + 0.8333333335 x = 2.271807895 + 0.8333333335 Combine like terms: 2.271807895 + 0.8333333335 = 3.1051412285 x = 3.1051412285 Simplifying x = 3.1051412285

Subproblem 2

x + -0.8333333335 = -2.271807895 Simplifying x + -0.8333333335 = -2.271807895 Reorder the terms: -0.8333333335 + x = -2.271807895 Solving -0.8333333335 + x = -2.271807895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -2.271807895 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -2.271807895 + 0.8333333335 x = -2.271807895 + 0.8333333335 Combine like terms: -2.271807895 + 0.8333333335 = -1.4384745615 x = -1.4384745615 Simplifying x = -1.4384745615

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.1051412285, -1.4384745615}

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